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The present study examines the elastic displacements in plain strained condition of involute cylindrical gears with asymmetric profile. A modification has been implemented of the elastic half space by means of the initial conditions of Hertz and the Frenkel problem has been modified for approximation of the involutes to the sides with wedges. The integration constants were derived, allowing determination of the total elastic displacement of the tooth along the various lines of engagement by the method of superposition. [ABSTRACT FROM AUTHOR]

This article is deduction of the necessary and sufficient condition for geometric synthesis of involute cylindrical gears with asymmetric profile of the teeth by the classic approach. The necessary condition is presented for slack-free engagement of the corresponding involutes along the initial circles and the crossing of the lines of engagement along the inter-center straight line, which is a new interpretation of the Willis's basic law of the flat engagement. [ABSTRACT FROM AUTHOR]